Information on Result #1022618
Linear OOA(8171, 177394, F81, 3, 19) (dual of [(177394, 3), 532111, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8116, 246, F81, 3, 9) (dual of [(246, 3), 722, 10]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(813, 82, F81, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;243,81) [i]
- linear OOA(814, 82, F81, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;242,81) [i]
- linear OOA(819, 82, F81, 3, 9) (dual of [(82, 3), 237, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;237,81) [i]
- linear OOA(813, 82, F81, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(8155, 177148, F81, 3, 19) (dual of [(177148, 3), 531389, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8155, 531444, F81, 19) (dual of [531444, 531389, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- OOA 3-folding [i] based on linear OA(8155, 531444, F81, 19) (dual of [531444, 531389, 20]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8171, 59131, F81, 21, 19) (dual of [(59131, 21), 1241680, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |